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Find the 11th term of the geometric sequence 6,-18,54...

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Answer:

11th term = 354294

Explanation:

The formula for the nth term of a geometric sequence is given by:


a_(n)=a_(1)*r^(^n^-^1^), where

  • a1 is the first term (i.e., 6 in this case),
  • r is the common ratio,
  • and n is the term position (e.g., 1st, 11th, etc.)

Finding the common ratio:

  • We can find the common ratio by dividing two consecutive terms.

Thus, we can find r by dividing -18 by 6:


r = -18/6\\\\r=-3

Thus, the common ratio is -3.

Finding the 11th term:

Now we can find the 11th term by substituting 6 for a1, -3 for r, and 11 for n in the formula for the nth term of a geometric sequence:


a_(11)=6(-3)^(^1^1^-^1^)\\\\ a_(11)=6(-3)^(^1^0^)\\\\ a_(11)=6(59049)\\\\ a_(11)=354294

Therefore, the 11th term of the geometric sequence is 354294.

User Mitchel Verschoof
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